Independent solution

How to solve this Arithmetically Increasing Coupons question

Setup

Setup

Use a 3% half-year yield for the fourteen coupon dates. Decompose each coupon into a level 22.50 component plus an arithmetic increase of X per period.

j=0.06/2=0.03,n=14j=0.06/2=0.03,\quad n=14

Model

Model

Price equals the level coupon annuity, X times the increasing-annuity factor, and the discounted redemption amount 300.

1050.50=22.50a14‾∣ j+X(Ia)14‾∣ j+300v141050.50=22.50a_{\overline{14}|\,j}+X(Ia)_{\overline{14}|\,j}+300v^{14}

Compute

Compute

After subtracting the fixed components from 1,050.50, division by the increasing-annuity factor gives X = 7.54.

X=7.54X=7.54

Answer

Answer

The calculation gives 7.54 for arithmetically increasing coupons, matching published choice A.

X=7.54(A)\boxed{X=7.54\quad\text{(A)}}